Axial-vector mass M A and K2K Q 2 distribution

22 June 2005 M.Sakuda@NuFact05

Axial-vector mass MA and K2K Q2 distribution

Makoto Sakuda (Okayama) 22 June, 2005 @ NuFact05

Outline1. MA analysis with SciFi detector data

R.Gran’s paper published in NuInt04 (NPB(Proc.Suppl.)139) M.Hasegawa et al.(K2K), --F.Sanchez’s talk

2. Summary

Discussion Session Review of the method to estimate the quasi-elastic cross sect

ion and the axial-vector mass MA


MA analysis with K2K SciFi detector data

Previous MA analyses generally used•Dipole form for vector form factors •Q2>0.2 (GeV/c)2 to avoid the nulcear effect

- Fermi-Gas model for nucleus (Deuteron wave function calculation for deuteron data) shows it.

In this analysis, we studied carefully the following effects:• Effect of the new vector form factor measurements• Effect of the energy scale (detector dep.) 1%~MA±0.05.

This may have been overlooked before.• Effect of background shape (1) from data• Proton rescattering –This is relevant to our QE/nQE separation• Flux uncertainty and event migration


1. Quasi-elastic cross section 　 np and form factors

A = Q2/4M2 [(4 + Q2/M2)|FA|2 - (4 - Q2/M2)|FV1|2

+ Q2/M2(1-Q2/4M2)|FV2|2+ 4Q2/M2ReFV*

1FV2

　　 -m2/4M2 (| FV1 + FV

2 |2 + | FV1 +2Fp |2 –4(1+) |Fp|2]

B = -Q2/M2ReF*A(FV

１ + FV２ ),

C = 1/4(|FA|2 + |FV1|2 + Q2/4M2|FV

2|2). Historically, we used Vector Form factors 　 GE

p=D, GMp=pD, GM

n=nD, GEn=nD,

D=1/(1+Q2/MV2)2, MV=0.843 (GeV/c2)

pn=5.6, = Q2/4M2

Axial-vector form factor FA

FA(Q2)=-1.2617/(1+Q2/MA2)2

Form Factors F1V,F2

V,and FA and (s-u)=4ME-Q2-M2

]u)-)(sC(Qu)-)(sB(Q -)[A(QdQ

d 22222

2

2

22

8

cos

E

GM cF


Nucleon Form Factors　　　

N Nq

e e

Electromagnetic current (Jaem) and weak hadronic charge

d current (JaCC=Va

1+i2–Aa1+i2) is written in terms of form

factors:

1

)()()(

1

)()()(

)()(2

1)(

4)()()(

)()()(

222

2

222

1

2

,

2

,

2(

,

2

22

2

2

1

2

2

2

2

1

2

QGQGQFand

QGQGQF

QGQGQG

M

QwithQFQFQG

QFQFQG

V

E

V

MVV

M

V

EV

n

ME

p

ME

V

ME

NNN

M

NNN

E

),()()()'()(||)'(

),()(2

)()'()(||)'(

),()(2

)()'()(||)'(

22

5

21

2

2

2

1

21

2

2

2

1

puQFqQFpupnApp

puQFqM

iQFpupnVpp

puQFqM

iQFpupNJpN

pA

i

VVi

NNem


dQE/dQ2 distribution at E = 1.3 GeV

Q2(GeV/c)2

dd

q2 (10

-38 c

m2 /

(GeV

/c)2 )

MA=1.2 GeVMA=1.1 GeVMA=1.0 GeV

Q2(GeV/c)2

Shape only

MA=1.0 GeV

MA=1.1 GeV

MA=1.2 GeV

AbsoluteCross-section

(includes normalization)


Nucleon Vector Form FactorsA simple dipole form GD = (1+Q2/MV

2) -2, MV=0.843was known to be good to only 10-20% level for vector Form Factors since 1970s. Gen looked finite.

But, no one needed better accuracy than that with dipole forms, untill Neutrino physics need it recently.

[email protected](‘74)


Updated Nucleon Vector Form Factors

A simple dipole form D=(1+Q2/MV

2) -2, MV=0.843GMnGMp GEp

Curve – Bosted, PRC51,409,’95Curve=(1+a1Q+a2Q2+.+a5Q5)-1

E.J.Brash et al. , Phys.Rev.C65,051001(2002). Similar

Neutrino cross section shape will change if we use these data.

Q2

de Jager@PANIC02


Old cross section (line) vs new (dot)

Ratio of new cross section to old cross section.

d/dQ2 vs. Q2 with new Vector Form Factors GMn,GMp,GEp ,GEN

+5%

-4%

Eν = 1.0

MA= 1.1

New cross section is smaller at low Q2 and larger at higher Q2

~5% overall difference in dQE

/dQ2

Fp is < 1% different, G

En is ~2% different, both largest at low Q2

Changes MA fit value by -0.05


Message from here is: Axial vector form factor can be approximated

by a dipole form only at 10-20% level as vector form factor was.

If the accurate neutrino cross section is measured in 5-10 years, there is no need for MA in the future. We parameterize axial form

factors in the same way.

Discussion What formalism should be preferable?


Q2 2E E p cos m2E

mN E m 2 2

m N E p cos

p muon momentum

muon angle w.r.t. beammN neutron massE muon energym muon mass

θ

p

２． Reconstruction of Quasi-Elastic Neutrino Interactionsfrom measured lepton angle and lepton momentum

FA Q2 FA 0 1 Q2 MA

2 2

Axial vector form factor depends on MA and Q2


To Muon Range Detector

Muon in the Muon Range Detector must have p

muon > 600 MeV/c

Recoil proton threshold isthree layers in SciFi p

proton > ~ 600 MeV/c

Scintillating Fiber (SciFi) detector-a Fine-grain detector with water target-It has operated since 1999 till the end of 2003 and measured flux

1-track events with muon only2-track events with muon plus either proton or pion


1 track event 2 track event

Event Selection n-> - p

Neutrino interaction in H2O target (+ 20% Aluminum)

Typical two-track event showing the muon and second track


+ n -> -+p

-

p

(E, p)

Expected protonassuming QE interaction

QE

use the location of proton track to separate events into three subsamples:

1-track (no proton) 60% QE 2-track QE enhanced 60% QE2-track nQE 85% nonQE, 15% QE

nonQE

distribution of 2 track events: QE and nonQE


Basic Distributions, P, for Scifi Detector

Overall agreement is good

One-track events (60% QE)

Muon momentum Muon angle

P


1 track sample 2 track QE enhanced 2 track non-QE

Reconstructed Q2 distribution in SciFi detectorMake DIS correction (Bodek/Yang) and reduced Coherent Pion production (Marteau)

Q2 (GeV/c)2 Q2 (GeV/c)2Q2 (GeV/c)2


Quasi Elastic fraction

Monte Carlo best fit

Fit only Q2 > 0.2 region

QE signal and inelastic backgroundare treated the same way

-> Q2 cutMost significantuncertainties dueto Pauli blockingand choice ofnuclear model,coherent pion,correction to DIS

Reconstructed Q2 (GeV/c)2


Free nucleon (no Pauli Blocking)

210kf = 225

235MeV/c

We Cut here

Uncertainty in QE cross section due to Pauli Blocking in the Q2 < 0.2 regiona Fermi-gas model with different Fermi-momenta k

f


Preliminary MA fit with K2K-I and K2K-IIa data

MA = 1.18 +/- 0.03 stat +/- 0.12 systBodek/Yang DIS correction and Marteau Coherent Pi cross-

section

1 Track 2 Track QE 2 Track nQEReconstructed Q2

Fit the 1track, 2track (QE), and 2track (nonQE) simultaneouslyK2K-I 8114 events total4310 Q2>0.2 in fitK2K-IIa 5967 events total 2525 Q2>0.2 in fit


Systematic Errors in combined fit

Flux and Normalization 0.08Energy scale 0.04LG density 0.02Escale/LG correlation 0.04Escale-MA correlation 0.03MA-1pi 0.03nQE/QE 0.03

Statistics 0.03

Total error 0.12


1.06

Zero Coherent pionLowers MA by 0.10better

Pauli Blocking0.10 effect atQ2min=0.0

Result is stable and consistent with MA=1.06 for cuts above Q2 = 0.2

But statistical errors dominate for high Q2 cutsThis is the standard cut used by almost all the experiments.

StandardCut

statistical errors and energy spectrumuncertainty

K2K-I data, MA-1 = 1.1

At low Q2 there are large nuclear effects (Pauli blocking)also uncertainty in coherent pion and multi-pion interactions.

MA vs Q2 cut value -- We use data for Q2>0.2


Q2 cut = 0.2

1.06

statistical errors only

MA for different energy ranges

The MA fit can be peformed separately for each energy range.They are consistent each other within 2 errors:

QE cross sections are consistent with MA=1.06 (GeV/c2) at each energy.


(H2O) This experiment

1.0MA

QE

Dipole Form FactorsQ2

min. = 0.2 (GeV/c)2

1.06 +/- 0.03 stat +/- 0.14 syst.

Comparison of MA obtained by other experiments

stat error total error

Deuterium


Conclusions

We present the preliminary analysis of MA

QE with SciFi detector (1999-2003)M

A = 1.18 +/- 0.03 stat. +/- 0.12 syst.

Here, we use Fermi Gas modl, the dipole form (MV=0.843) for vector form factors, and only data with Q2 > 0.2.

●We will give two values of MA, one with old vector form factors in order to compare with the old MA measurements, and the other with new vector form factors. MA becomes smaller by 0.05-0.07.

----------------------------------------------Personal comment:●In the near future, we need better parametrization for the quasi-elastic cross sections (single pion production) and better theoretical calculations over the entire q2 region, if we want to obtain the accuracy at a few % level.●BodekVector form factors and nuclear effect will be measured. e+Ce+X.June 25 (WG2)●Benhar, Varverde,BarbaroBetter calculation over the entire q2 region. ●Benhar et.al,hep-ph/0506116, to appear in PRD.


Benhar et al., hep-ph/0506116, PRD,-Comparison of FG, SP, SP+FSI validated by electron scattering data

FG

SP

SP+FSI


Combined fit with the K2K-I dataQ2 distribution, all energy bins combined, no Coherent Pion in MC

Green shows the QE fraction

Slide 4a


Q2 distribution, all energy bins combined, no Coherent Pion in MCGreen shows the QE fraction

Combined fit with the K2K-IIa data

Slide 4b


Pauli Bloching effect

Quasi-elastic

production

W/o Pauli effect

W/ Pauli effect

10-15% suppression At low Q2

Total 3% reduction

E=1.3 GeV ， kF=220 MeV/c

Pp

Pp

q

W

np

Pp

q

If P <kF , suppressed.

Total 8%

Nuclear effects are large in the low Q2 region, where the cross section is large.

d/dQ2

d/dQ2 0.5 1.0


Charged-Current Quasi-elastic Scattering

This is the simplest and the most important reaction. Calculation by Ch.L.Smith et al. with MA=1.0.

np)pn)

1x10-381.0(cm2)

0.0.1 1.0 10. 10.50. 1.0.1

1.0

Pauli effect ~8%


Single Pion Production Cross Section

Prediction = Rein-Sehgal MA=1.2 GeV/c2

1x10-381.0(cm2)

0.0

MS@nuint01

Documents

Axial-vector mass M A and K2K Q 2 distribution